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# Accession Number:

## AD0701156

# Title:

## CONVEXITY PRESERVING SCALE TRANSFORMATIONS,

# Descriptive Note:

# Corporate Author:

## BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

# Report Date:

## 1969-12-01

# Pagination or Media Count:

##
18.0

# Abstract:

## Let C be the class of increasing convex functions on the interval from zero to but less than infinity with f0 0. Then f epsilon C implies that the composition psifpsi superscript-1 epsilon C if and only if psix cx to the power p, c 0, p or 1. Functions psi for which psifpsi superscript-1 epsilon C whenever f epsilon C are characterized for various other classes C, e.g., the concave, starshaped or superadditive increasing functions f on the interval from zero to but less than infinity with f0 0. In addition, classes of functions on other domains, and logarithmically convex or concave functions are also considered. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#